3x(5x+2)=8x+20

Solution for 3x(5x+2)=8x+20 equation:

3x(5x+2)=8x+20

We move all terms to the left:

3x(5x+2)-(8x+20)=0

We multiply parentheses

15x^2+6x-(8x+20)=0

We get rid of parentheses

15x^2+6x-8x-20=0

We add all the numbers together, and all the variables

15x^2-2x-20=0

a = 15; b = -2; c = -20;
Δ = b2-4ac
Δ = -22-4·15·(-20)
Δ = 1204
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1204}=\sqrt{4*301}=\sqrt{4}*\sqrt{301}=2\sqrt{301}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{301}}{2*15}=\frac{2-2\sqrt{301}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{301}}{2*15}=\frac{2+2\sqrt{301}}{30}
$